Question

The diameter of the two circular plates is $10\text{cm}$ and $24\text{cm}$ respectively. What is the diameter of the plate which has an area equal to the combined area of the two given plates?

Answer 1

Let the diameter of the first circle be $d_1$ and radius $r_1$ and area is equal to $A_1$.

$d_1=10\text{cm}$

$\Rightarrow r_1=5\text{cm}$

$A_1=\pi (5{)}^2$

$=25\pi {\text{cm}}^2$

Let the diameter of the first circle be $d_1$ and radius $r_1$ and area is equal to $A_1$.

$d_2=24\text{cm}$

$\Rightarrow r_2=12\text{cm}$

$A_2=\pi (12{)}^2$

$=144\pi {\text{cm}}^2$

Let the radius of the plate whose area is $A$ be $r$ then,

$\begin{array}{cc}A& =A_1+A_2\\ \pi r^2& =25\pi +144\pi \\ r^2& =169\\ r& =13\text{cm}\end{array}$